With the advancement of electric vehicle (EV) technology and growing market demand, EVs have become a key trend in the green transformation of transportation. In the context of renewable energy, Vehicle-to-Grid (V2G) technology has emerged as an important tool for intelligent energy management. However, the fairness, privacy, and security issues have become increasingly prominent in its application. To address these challenges, we propose V2G-SSEx, a privacy-preserving fair exchange scheme for V2G transactions that combines zero-knowledge proofs and smart contract technology to achieve both transaction fairness and privacy in this paper. The proposed scheme introduces a supervisory role and designs incentive mechanisms and random selection algorithms to ensure transaction security and behavior supervision. Through experiments based on Solidity and ZoKrates, the scheme demonstrates superior performance in terms of computational cost, latency, and stability.